The minima are reached for m values given in A147804.

This is related to the abc conjecture, see also A143702, A147801, A147800 (2^n, 3^n, 5^n analogs) and A147298 (general case).

All terms of this sequence are even, so one could also consider A147799/2 = 3, 3, 15, 15, 141, 1131, 8517, 18003, 35535, ... So far these terms are also multiples of 3, but this might be a coincidence.